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  • article
    CHU Jiacheng, TANG Yanlin
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(3): 455. https://doi.org/10.3969/j.issn.1001-4268.2023.03.010
    We review some results on the recent development of statistical inference for high-dimensional linear models. We introduce three debiased LASSO estimators, which are asymptotically normal and thus we can construct statistical inference for low dimensional parameters in high-dimensional setting. In addition, we give a brief introduction to the bootstrap assistant procedures to conduct simultaneous inference based on the debiased LASSO.
  • CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(2): 315.
  • article
    WU Zhen, ZHANG Detao
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(3): 413-435. https://doi.org/10.3969/j.issn.1001-4268.2023.03.007
    In this paper, based on the basic theory and application background of stochastic differential equation and backward stochastic differential equation, and combined with stochastic optimal control theory and option price theory in financial market, we will derive the general form of fully coupled forward backward stochastic differential equations (FBSDEs in short). From the point of view of the solvability of this kind of equations, the existing methodology in the literature are analyzed and discussed, a ``unified framework'' approach is introduced to guarantee the existence and uniqueness of solutions for non-Markovian FBSDEs, and several further properties of FBSDEs are obtained. A linear transformation method in virtue of the non-degeneracy of transformation matrix is introduced for cases that the linear FBSDEs, as an important supplement and improvement of the ``unified approach'' method, which makes the application of FBSDEs more extensive.
  • article
    ZHANG Yingying, RONG Tengzhong, LI Manman
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(2): 159-177. https://doi.org/10.3969/j.issn.1001-4268.2023.02.001
    The proposed power-power loss function which has balanced convergence rates or penalties for its argument too large and too small, has all the seven properties listed in this paper, and thus it is recommended to use for the positive restricted parameter space. We then calculate the Bayes estimator, the posterior risk, the integrated risk, and the Bayes risk of the parameter under the power-power loss function. After that, we analytically calculate these quantities under a hierarchical normal and normal-inverse-gamma model. Finally, the numerical simulations
    exemplify our theoretical studies.
  • article
    LIU Zhiwei, XIA Zhiming
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(2): 218-238. https://doi.org/10.3969/j.issn.1001-4268.2023.02.004
    Based on the poor interpretability and the limitation of summarizing the overall trends and local changes at the same time of the traditional neural network, it is not suitable for estimating the regression function of the partial linear model directly. In response to this problem, the semi-linear neural network structure that has both linear and non-linear parts is constructed firstly. Then, the consistency of the network estimator based on empirical risk minimization is proved under some necessary conditions, and the semi-linear network parameter estimation algorithm based on gradient descent is designed, which is called as the local back propagation algorithm. The random simulation experiments verify the large sample property, the results of the case analysis explain the necessity of introducing a linear part in the neural network. In particular, the experiment shows that the estimation effect of this method is slightly better than the N-W kernel estimation method based on the Boston House Price Dataset.
  • article
    MI Hui, DI Wenrong, LIN Jinguan
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(2): 239-258. https://doi.org/10.3969/j.issn.1001-4268.2023.02.005
    This paper studies an optimal investment and reinsurance problem in which the interest rate is driven by the Vasicek process, the surplus process is governed by a diffusion approximation model and two dependent classes of insurance business correlated through a common shock component are considered. The objective of the insurer is to minimize the variance of terminal wealth for a given terminal expected wealth. By using the stochastic linear-quadratic (LQ) control theory and the corresponding Hamilton-Jacobi-Bellman (HJB) equation, we obtain the explicit expressions for the value function, and the optimal investment and reinsurance strategies. Furthermore, the efficient strategies and efficient frontier are derived explicitly. Finally, some examples are given to show the influence of model parameters on the optimal investment and reinsurance strategies.
  • article
    SHI Yanjie, PENG Xiuyun, LIU Wenbo
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(3): 317-332. https://doi.org/10.3969/j.issn.1001-4268.2023.03.001
    The reliability of k/n system with two interrelated competitive failure mechanisms leading to component failure is considered. The competitive correlation is connected by Gumbel-Barnett (GB) Copula with Weibull marginal distributions that have different scale
    parameters and shape parameters. The effects of GB Copula on the failure rate and reliability of components and k/n system are studied when the shape parameters are equal. We proved that the components have increasing, decreasing and bathtub failure rate in terms of the same shape parameter but different values. The reliability of the k/n (n>1) system is not consistently superior to that of the simple system (i.e., k/n=1/1).Based on progressively Type-II censored samples, the Bayes estimation of the parameters and reliability of the k/n system are discussed, and Monte Carlo experiments are carried out to illustrate proposed methods. Finally, a real-life data is provided to demonstrate the model and method proposed in this paper.
  • article
    YANG Wenwan, YUAN Cheng
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(3): 449-454. https://doi.org/10.3969/j.issn.1001-4268.2023.03.009
    We present a weighted version of the second Borel-Cantelli lemma, which complements two earlier generalizations of this lemma.
  • article
    ZHANG Yinqiu, LV Guangying, JIAO Junjun
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(3): 333-346. https://doi.org/10.3969/j.issn.1001-4268.2023.03.002
    In this paper, the Lotka-Volterra stochastic predator-prey systems in a polluted environment is considered. The existence and global attractivity of the periodic solutions are obtained. Furthermore, we obtain the sufficient conditions for the existence and global attractivity of a nontrivial positive periodic solution. Finally, simulations verify our analytical results.
  • CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS.
    Accepted: 2023-06-16
  • article
    JIAO Junjun, CHENG Weihu
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(2): 178-196. https://doi.org/10.3969/j.issn.1001-4268.2023.02.002
    In this paper, the reliability of a system is discussed when the strength of the system and the stress imposed on it are independent, non-identical binomial exponential 2 distributed random variables. Different methods for estimating the reliability are applied. The maximum likelihood (ML), Wilson-Hilferty (WH) normal-based approximation and Bayesian methods are used in the estimation procedure. Also, we propose confidence intervals of the stress-strength reliability based on the approximate method, Bayesian method and Bootstrap methods (Boot-p and Boot-t). Different methods and the corresponding confidence intervals are
    compared using Monte-Carlo simulations. Finally, analysis of a real data set is presented for illustrative purposes.
  • article
    LIU Xuan, MA Haiqiang
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(4): 475-490. https://doi.org/10.3969/j.issn.1001-4268.2023.04.001
    In this paper, we consider the change-point problems for the functional linear model, where the explanatory variable is a random process, and the response is a scalar. Based on the projecting moment estimators of the parameters onto the truncated finite-dimensional space, we propose the detecting statistic and give the estimator of the change-point. In a theoretical investigation, we derive the asymptotic distribution for the proposed detecting statistic, and establish the consistency of the change-point estimate under some mild conditions. Some simulation studies and a real data analysis are conducted to illustrate the finite performance of the proposed testing methods.
  • article
    CHENG Gongpin, WANG Qinghua, YAO Dingjun
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(2): 283-300. https://doi.org/10.3969/j.issn.1001-4268.2023.02.007
    With the deepening of population aging in China, the pricing method of long-term care insurance for the elderly has become a hot issue in actuarial direction. Based on the data of CLHLS from 2014 to 2018, the health statuses of the elderly are further divided into six states on the basis of the traditional three and four state Markov model. It uses the Markov model to calculate the value of each state. The transition strength matrix and transition probability matrix of health state are solved by Robinson power function, which takes gender and age into account. Then, the premium years of 65, 75 and 85 years old are estimated by using double random Lee-Carter model, random walk model and life expectancy formula, which provides a theoretical reference for the pricing of long-term care insurance in China.
  • CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS.
    Accepted: 2023-06-16
  • article
    PAN Yingli, XU Kaidong, CHEN Huifang, LIU Zhan
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(3): 394-412. https://doi.org/10.3969/j.issn.1001-4268.2023.03.006
    Cox model is one of the most popular semi-parametric regression models in epidemiology, biomedical science and clinical trials. In the modeling process, the observed covariates are usually contaminated, and the pollution factor can be measured, but the pollution function is unknown. Therefore, the direct use of the contaminated covariate for parameter estimation may lead to incorrect statistical inference. Researchers often find the best time for disease treatment, and omission of such survival information may lead to a decrease in the estimated effectiveness. In this paper, an improved estimation of the Cox model with contaminated covariates and auxiliary survival information is studied. Kernel smoothing method is used to calibrate the contaminated covariates, and auxiliary survival information is extracted by grouping for parameter estimation. Then, generalized moment estimation method is used to solve the problem of hyperdimensional equations. The results of simulation analysis and empirical study show that the generalized moment estimation method based on the Cox model with covariate calibration is better than the partial likelihood estimation method and the generalized moment estimation method based on the Cox model with the unadjusted covariates.
  • CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS.
    Accepted: 2023-06-16
  • article
    XIE Jiayi, ZHANG Zhimin
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(2): 197-217. https://doi.org/10.3969/j.issn.1001-4268.2023.02.003
    In this paper, we study the statistical estimation of the discounted density function of the deficit at ruin in the compound Poisson model with barrier dividend strategy. When both the Poisson intensity for the claim number process and the density function for the individual claim sizes are unknown, we use the COS method to construct the estimator. Under a large sample setting, we derive consistency property of the estimator. We also provide simulation results to verify the effectiveness of this estimation method when the sample size is finite.
  • article
    ZHOU Hao, PENG Xingchun
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(3): 363-382. https://doi.org/10.3969/j.issn.1001-4268.2023.03.004
    This paper studies the time-consistent investment strategy of DC pensions with premium return clauses under partial information. We assume that pension managers only have partial information about stock, that is, they can only observe the price of the stock, but not the rate of return of the stock. The pension has a premium return clause. If the insured person dies during the fund accumulation period, the premium paid by him needs to be refunded. In addition, this article also considers inflation and random wages. First, using the Kalman filter theory, the optimal portfolio problem under the partial information situation is transformed into a problem under the complete information situation. Then, by solving an extended HJB equation, the time-consistent investment strategy and the optimal value function are obtained, and a parametric formula of the mean-variance effective frontier is derived. Finally, using the Monte Carlo method to perform numerical simulations, we analyze the effects of partial information and premium return clauses on the stock investment ratio and effective frontier, and give corresponding economic explanations.
  • article
    ZHANG Yi
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(2): 301-314. https://doi.org/10.3969/j.issn.1001-4268.2023.02.008
    The expected utility theory is one of the important methods to determine the premium of the risks. This paper establishes the Bayesian model of the expected utility premium principle. We defines the risk premium under the expected utility principle, and gives the Bayesian estimation and credibility estimation of the risk premium. Furthermore, the statistical properties of the estimates are considered. Finally, the asymptotic normality and convergence rate of risk premium estimation is verified by numerical simulation.
  • article
    WEN Limin, HAN Fei
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(3): 347-362. https://doi.org/10.3969/j.issn.1001-4268.2023.03.003
    Retrospective premium is a premium rating plan that relies on the actual loss of the insurer during the policy period. It underwrites losses that have occurred in the past. The retrospective premium has been used in the reinsurance model in this paper. When the
    optimal criterion is to minimize the risk-adjusted value and the risk capital is measured by TVaR, the optimal ceded function under this model is in the form of stop-loss reinsurance. The minimum risk-adjusted value and the optimal retention have been obtained. Finally, through numerical simulation, we assumed that the loss has the exponential distribution, Pareto distribution and Gamma distribution, and explored the influence of the tax multiplier T and the parameter \rho on the optimal retention and the minimum risk adjusted-value. The results show that when other parameters are constant, as T increases, the optimal retention increases and the minimum risk-adjusted value decreases, and when other parameters are constant, the optimal retention and the minimum risk-adjusted value both increase with the increase of \rho. 
  • article
    YANG Xin, YANG Shanchao, XING Guodong, YANG Xiutao
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(3): 383-393. https://doi.org/10.3969/j.issn.1001-4268.2023.03.005
    The volatility of asset prices is an important research topic that scholars pay close attention to. In recent years, scholars have proposed many estimation methods for volatility, and studied the consistency and asymptotic normality of the estimators. In this paper, we focuses on the NW type kernel estimator of spot volatility proposed by Kristensen\ucite{26}, points out that there are some errors in the relevant proof process, and derives further the strong consistency and uniform strong consistency of the estimator under some reasonable conditions. 
  • article
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(6): 924-940. https://doi.org/10.3969/j.issn.1001-4268.2023.06.010
  • article
    WEN Xin, XU Xiaoya, GUO Xianping
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(4): 589-603. https://doi.org/10.3969/j.issn.1001-4268.2023.04.009
    This paper considers a risk probability minimization problem for nonstationary discrete-time Markov decision processes, in which the transition probabilities and the reward functions depend on time. Different from the expected reward/cost criteria in the existing literature, the optimality performance here is to minimize the probability that the total rewards do not reach a given profit goal until the first passage time to some target set. Under mild reasonable conditions, we establish the corresponding optimality equations, verify that the sequence of the optimal risk functions is the unique solution to the optimality equations, and prove the existence of an optimal Markov policy.
  • article
    CHEN Mengyao, DAI Wei, JIN Baisuo
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(4): 491. https://doi.org/10.3969/j.issn.1001-4268.2023.04.002
    For high-dimension spatial regression problems, we propose a effective sparse Bayesian model. By introducing a hierarchical Gaussian Markov random field prior, the model can obtain sparse spatial varying parameters, and meanwhile, it can obtain homogeneous parameters estimation for adjacent spatial regions. We use a fast-converging variational EM algorithm for posterior inference, rather than the traditional sampling-based methods. In the M-step of the algorithm, the optimization can be transformed into a classic adaptive lasso problem by simple deformation. The simulation result demonstrate the better performance of our model both in parameters estimation and variable selection. Finally, the proposed model is used to analyze the impact of the socio-demographic factors on the death rate of the COVID-19 in countries of Europe.
  • article
    DONG Yinghui, WEI Siyuan, YIN Zihan
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(2): 259-282. https://doi.org/10.3969/j.issn.1001-4268.2023.02.006
    From the dual perspective of the insurer and the insured, we investigate an optimal investment problem with short-selling and two-VaR constraints faced by the insurer who offers participating contracts. This analysis is particularly relevant for an insurance company operating under the Solvency II regulation which aims to maximize the expected  utility of the terminal payoff to the insurer, while at the same time being required to provide its policyholders a minimum guaranteed amount and a bonus. We adopt a dual control approach and a concavification technique to solve the problem and derive the representations of the optimal terminal wealth. We also carry out some numerical analysis to show that in contrast to one-VaR constraint that we consider only from the perspective of the insurer or the insured, two-VaR constraint that we consider from the dual perspective can strictly improve the risk management for bad economic states and decrease the moral risk.
  • article
    SUN Hongyan, WANG Huaming
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(5): 633-642. https://doi.org/10.3969/j.issn.1001-4268.2023.05.001
    Consider a nearest-neighbor random walk with certain asymptotically zero drift on the positive half line. Let $M$ be the maximum of an excursion starting from 1 and ending at 0. We study the distribution of M and characterize its asymptotics, which is quite different from those of simple random walks.
  • article
    YANG Xiaorong, LI Lu, WU Haoyue, XU Wenting
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(4): 604-622. https://doi.org/10.3969/j.issn.1001-4268.2023.04.010
    In this paper, for a widely applicable semi-parametric model, partially linear additive model, we study the estimation of its coefficients and nonparametric functions when responses are censored. For this, a composite quantile regression estimation method based on data augmentation is proposed. This method utilizes the relationship between quantile regression and distribution function to construct the imputation dataset, and the final estimators are obtained by composite quantile regression through iterations. The proposed method relaxes the assumptions of the model, not only has low requirements for initial values of iterations but also allows the case when different types of censoring are present in the same dataset. Numerical simulations
    show that the proposed method can accurately estimate the coefficients and nonparametric functions of the censored partially linear additive model. In real data analysis, this paper studies the air quality in Beijing, and measures the effects of PM10 concentration, CO concentration, temperature, air pressure, and dew point on PM2.5 concentration. The results show that the composite quantile regression of the partially linear additive model can describe well the influence of these factors on PM2.5 from the perspective of linear and nonlinear relationships, and the proposed method performs well in the processing of censored data.
  • article
    CHEN Jinshu, TANG Yuling
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(3): 436-448. https://doi.org/10.3969/j.issn.1001-4268.2023.03.008
    Let M be a discrete-time normal martingale satisfying some mild conditions, \mathscr{S}(M)\subset L^2(M)\subset \mathscr{S}^*(M) be the Gel'fand triple constructed from the functionals of M. \mathscr{L} denote the space of continuous linear operators from the testing functional space $\mathscr{S}(M)$ to the generalized functional space \mathscr{S}^*(M). As is known, the usual product in \mathscr{L} may not make sense. However, by using the 2D-Fock transform, one can introduce convolution in \mathscr{L}, then one can try to introduce a Bochner-style integral for \mathscr{L}-valued functions with respect to \mathscr{L}-valued measures in the sense of convolution. This paper just studies such a type of integral. First, a class of \mathscr{L}-valued measures are introduced and their basic properties are examined. Then, an integral of an \mathscr{L}-valued function with respect to an $\mathscr{L}$-valued measure is defined and a dominated convergence theorem is established for this integral. Finally, a convolution measure of two \mathscr{L}-valued measures is also discussed and a Fubini type theorem is proved for this integral.
  • article
    GUO Yunrui, LIANG Xiaoqing
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(4): 531-546. https://doi.org/10.3969/j.issn.1001-4268.2023.04.005
    We consider an optimal robust investment problem for a defined contribution DC pension plan with stochastic income and
    model uncertainty. In the model, the pension account is allowed to invest into a risky asset and a risk-free asset, and the dynamic of the price of risky asset follows a Heston model. The objective of the problem is to maximize the expected utility of the terminal relative wealth by choosing admissible investment strategies. By using the stochastic control dynamic programming approach, we find the robust optimal investment strategy and the corresponding value function when the utility function has the power or the exponential form, respectively. At last, we show a numerical example to further analyze the theoretical results through the MATLAB software.
  • article
    ZHANG Bo, LIU Chaolin, YU Wenguang, LI Jing
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(5): 643-658. https://doi.org/10.3969/j.issn.1001-4268.2023.05.002
    In this paper, we consider the nonparametric estimation of the ruin probability in a compound Poisson risk model perturbed by diffusion. We approximate the ruin probability based on the complex Fourier series expansion (CFS) method, and use a random sample on claim number and individual claim sizes to construct a nonparametric estimator of the ruin probability. We also perform an error analysis of the estimator under a large sample size, and provide simulation results to verify the effectiveness of this estimation method under a finite sample size.
  • article
    LIN Hongmei, ZHANG Shaodong, PENG Yiluo, DU Jinyan
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(4): 561-576. https://doi.org/10.3969/j.issn.1001-4268.2023.04.007
    Longitudinal data is an important type of data that is widely used in sociology, economics, biomedicine, epidemiology and other fields. However, in practical problems, people often encounter the situation that the variable dimension is very high and the variable concerned cannot be directly observed, that is, there is a measurement error. In order to solve such problems, this paper studies the estimation of the longitudinal data order index model with measurement error. Based on local linear method and simulation extrapolation (SIMEX) method, this paper constructs a new method for estimating single-index parameters and nonparametric link functions. The effectiveness of the proposed estimation method is verified by Monte Carlo numerical simulation. Compared with the Naive estimation which ignores the measurement error and the estimation which ignores the intra-individual correlation, the estimation constructed in this paper has a smaller mean square error. Finally, we apply the method in this paper to the actual data analysis of the investment demand of listed companies, and the results show that the measurement error has a significant impact on the parameter estimation in practical problems.
  • article
    LI Jinfeng, JIANG Yifan, DU Kai
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(4): 517-530. https://doi.org/10.3969/j.issn.1001-4268.2023.04.004
    We study the numerical solutions for a class of coupled mean-field forward-backward stochastic differential equations. Under suitable regularity assumptions, a posteriori estimate of forward-backward stochastic differential equation is provided. This posterior estimate indicates that the error of the solution for the forward-backward equation can be controlled by the error of the terminal term. Furthermore, we propose a numerical algorithm based on deep neural network and conduct convergence analysis on the discretization scheme.
  • article
    YANG Menglan, YANG Shuzhen
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(4): 623-632. https://doi.org/10.3969/j.issn.1001-4268.2023.04.011
    In financial market, VaR and ES are applied to measure the risk of asset, portfolio management and margin calculation, which are the international unified standards for bank capital and risk supervision. However, VaR has some certain limitations, ES, as an important risk measurement method, has attracted the attention of financial institutions in recent years. Based on the sublinear expectation theory and G-VaR, this study proposes a new calculation method for ES, and denoted as G-ES. This calculation method can be naturally combined with the back testing of G-VaR. Based on the data of S\&P 500 index and CSI300 index, comparing with other commonly used models, such as historical simulation, AR-GARCH model and POT model based on extreme value theory, it is found that this G-ES method has a good performance within different historical data windows.
  • article
    SONG Zihao, HAN Miao
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(4): 547-560. https://doi.org/10.3969/j.issn.1001-4268.2023.04.006
    The pricing problem of correlation options with exchange rate risk under the regime-switching jump-diffusion model is studied. Under the risk neutral measure, it is assumed that the exchange rate follows the regime-switching mean reversion model and the asset prices follow the regime-switching jump-diffusion models. The pricing formula of the correlation options with exchange rate risk is derived by using the measure transform and Fourier transform method. Moreover, the numerical results of option value are provided by the fast Fourier transform algorithm, and the effects of different models and some important parameters on the value of correlation options with exchange rate risk are analyzed.
  • article
    MU Wanying, WANG Xinyi, FENG Zhenghui
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(5): 667-681. https://doi.org/10.3969/j.issn.1001-4268.2023.05.004
    Currently, spectroscopy technology is widely used in traditional Chinese medicine analysis. In this paper, from the functional
    data analysis perspective, we study outlier detection methods for spectral data, detect outliers, and propose the ``Oja depth detection method''. Simulation studies demonstrate the advantages of the Oja depth detection method. We compare the Oja depth detection method with three existing methods on a Chinese medicine spectral data of 73-dose six-mixture liquid. The results show the proposed Oja depth method is able to detect all six unqualified samples and has the highest accuracy.
  • article
    WEN Xian, HUO Haifeng
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(4): 577-588. https://doi.org/10.3969/j.issn.1001-4268.2023.04.008
    This paper concerns the exponential utility maximization problem for semi-Markov decision process with Borel state and action spaces, and nonnegative rewards. The optimal criterion is maximize the expectation of exponential utility of the total rewards
    in infinite horizon. Under the regular and compactness-continuity conditions, we establish the corresponding optimality equation, and prove the existence of an exponential utility optimal stationary policy by an invariant embedding technique. Moreover, we provide an iterative algorithm for calculating the value function as well as the optimal policies. Finally, we illustrate the computational aspects of an optimal policy with an example. 
  • article
    SHI Xueni, DA Gaofeng
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(5): 747-764. https://doi.org/10.3969/j.issn.1001-4268.2023.05.009
    The probabilistic combination method is a very useful method to analyze the reliability of wireless sensor network (WSN), and it can effectively deal with the isolation effect and competition failure in the network. However, there are some shortcomings in the reliability modeling and calculation of WSN based on the probabilistic combination method in the existing literature, which leads to a limited application of the research results and even an incorrect evaluation for the reliability of WSN. This paper studies the reliability modeling and calculation of a typical WSN which has only one relay node and the probabilistic functional dependence mechanism. Under the general assumption that WSN faces local failures of components and global failures caused by external attacks, a reliability model that is more realistic and more rigorous is established for WSN. Based on rigorous probability combination analysis, it shows systematic method and compact formulas for the reliability of WSN. The current study enhances the research on such issues in the literature efficiently. Finally, as applications, we calculate the reliability of two special WSNs ---body sensor network and air monitoring system.
  • article
    ZHENG Qunzhen, FENG Pinghua, ZHANG Hongbo
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(4): 506. https://doi.org/10.3969/j.issn.1001-4268.2023.04.003
    In this paper we study a discrete-time Geo/T-IPH/1 queue model, where T-IPH denotes the discrete-time phase type distribution defined on a birth and death process with countably many states. The queue model can be described by a quasi-birth-and-death (QBD) process with countably many phases. Using operator-geometric solution method, we first give the expression of the joint stationary distribution. Then we obtain the explicit stationary queue length distribution of the queue we considered. Finally, a numerical example is also presented to illustrate the computational procedure.
  • article
    QUAN Zhuojun, ZHENG Ming, YU Wen
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(5): 730-746. https://doi.org/10.3969/j.issn.1001-4268.2023.05.008
    Semi-supervised data contains a labeled data set with both responses and covariates and an unlabeled data set with covariates only. The inference based on semi-supervised data is gaining more and more interests in statistics. When the response in the labeled data is binary, case-control sampling is commonly used to alleviate the imbalanced data structure. When the response and the covariates satisfy the logistic model, the slope parameter of the model can be consistently estimated even for the case-control sampling. However, when the logistic model is incorrectly specified for the data, the case-control samples can not estimate the population risk minimizer consistently. With the help of the unlabeled data, we derive a consistent estimator for the case population proportion. Then, an inverse probability weighted loss function is developed to obtain a consistent estimator for the population risk minimizer. The proposed estimators are shown to be asymptotically normal and the limiting variance-covariance matrix can be consistently estimated. Simulation results show that the proposed method gives out reasonable finite sample performances. A real data example is also analyzed for illustration.
  • article
    QIU Dehua, ZHAO Qianjun
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS. 2023, 39(5): 659-666. https://doi.org/10.3969/j.issn.1001-4268.2023.05.003
    Let \{X,X_n,n\geq1\} be a sequence of identically distributed NA random variables and set S_n=\sum_{i=1}^nX_i, n\geq 1. Let h(\cdot) be a positive nondecreasing function on (0,\infty) such that \int_1^\infty[th(t)]^{-1}\md t=\infty. Denote Lt=\ln\max\{e,t\}, S_n=\sum_{i=1}^nX_i, \psi(t)=\int_1^t[sh(s)]^{-1}\md s, t\geq 1. In this paper, we prove that \sum_{n=1}^\infty[nh(n)]^{-1}\pr(\max_{1\leq j\leq n}|S_j|\geq (1+\varepsilon)\sigma\sqrt{2nL\psi(n)})<\infty, \forall\,\varepsilon>0 if and if \ep(X)=0 and \ep(X^2)=\sigma^2\in(0,\infty). The result partially extends and improves the theorems of \ncite{7}.